The typical cycle for apartment hunting

Hi, I am new to the process of searching for an apartment online. I am targeting March 1st but I am currently month to month so fortunately I am not under too much pressure to move by then. However I would really like to secure something as I need to get out of here sooner rather than later. Anyway I see that every hour I message not through any of the websites are generally looking for Feb 1st which ain’t happening. So I figure as of next week they will all be open to March 1st. When do people typically like to secure a place by? I assume the earlier in the month the better so as to have enough time to actually move. All this seems super overwhelming to be honest and I guess I have been extremely privileged to have always found my apartments through word of mouth and friends. Anyway just trying to gain a little perspective as we head in to another month of the chaos that is apartment hunting in NYC. I appreciate any feedback.

Thanks